IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v190y2021i1d10.1007_s10957-021-01879-y.html
   My bibliography  Save this article

Optimality Conditions and Exact Penalty for Mathematical Programs with Switching Constraints

Author

Listed:
  • Yan-Chao Liang

    (Henan Normal University)

  • Jane J. Ye

    (University of Victoria)

Abstract

In this paper, we give an overview on optimality conditions and exact penalization for the mathematical program with switching constraints (MPSC). MPSC is a new class of optimization problems with important applications. It is well known that if MPSC is treated as a standard nonlinear program, some of the usual constraint qualifications may fail. To deal with this issue, one could reformulate it as a mathematical program with disjunctive constraints (MPDC). In this paper, we first survey recent results on constraint qualifications and optimality conditions for MPDC, then apply them to MPSC. Moreover, we provide two types of sufficient conditions for the local error bound and exact penalty results for MPSC. One comes from the directional quasi-normality for MPDC, and the other is obtained via the local decomposition approach.

Suggested Citation

  • Yan-Chao Liang & Jane J. Ye, 2021. "Optimality Conditions and Exact Penalty for Mathematical Programs with Switching Constraints," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 1-31, July.
    • Handle: RePEc:spr:joptap:v:190:y:2021:i:1:d:10.1007_s10957-021-01879-y
    DOI: 10.1007/s10957-021-01879-y
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-021-01879-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-021-01879-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lei Guo & Jin Zhang & Gui-Hua Lin, 2014. "New Results on Constraint Qualifications for Nonlinear Extremum Problems and Extensions," Journal of Optimization Theory and Applications, Springer, vol. 163(3), pages 737-754, December.
    2. Falk Hante & Sebastian Sager, 2013. "Relaxation methods for mixed-integer optimal control of partial differential equations," Computational Optimization and Applications, Springer, vol. 55(1), pages 197-225, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kin Keung Lai & Shashi Kant Mishra & Sanjeev Kumar Singh & Mohd Hassan, 2022. "Stationary Conditions and Characterizations of Solution Sets for Interval-Valued Tightened Nonlinear Problems," Mathematics, MDPI, vol. 10(15), pages 1-16, August.
    2. Jinman Lv & Zhenhua Peng & Zhongping Wan, 2021. "Optimality Conditions, Qualifications and Approximation Method for a Class of Non-Lipschitz Mathematical Programs with Switching Constraints," Mathematics, MDPI, vol. 9(22), pages 1-20, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Marvin Severitt & Paul Manns, 2023. "Efficient Solution of Discrete Subproblems Arising in Integer Optimal Control with Total Variation Regularization," INFORMS Journal on Computing, INFORMS, vol. 35(4), pages 869-885, July.
    2. Martin Siebenborn, 2018. "A Shape Optimization Algorithm for Interface Identification Allowing Topological Changes," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 306-328, May.
    3. S. Göttlich & A. Potschka & C. Teuber, 2019. "A partial outer convexification approach to control transmission lines," Computational Optimization and Applications, Springer, vol. 72(2), pages 431-456, March.
    4. Leonid Minchenko, 2019. "Note on Mangasarian–Fromovitz-Like Constraint Qualifications," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1199-1204, September.
    5. Falk M. Hante & Martin Schmidt, 2019. "Complementarity-based nonlinear programming techniques for optimal mixing in gas networks," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 7(3), pages 299-323, September.
    6. Giorgio Giorgi, 2018. "A Guided Tour in Constraint Qualifications for Nonlinear Programming under Differentiability Assumptions," DEM Working Papers Series 160, University of Pavia, Department of Economics and Management.
    7. Sven Leyffer & Paul Manns & Malte Winckler, 2021. "Convergence of sum-up rounding schemes for cloaking problems governed by the Helmholtz equation," Computational Optimization and Applications, Springer, vol. 79(1), pages 193-221, May.
    8. Mengwei Xu & Jane J. Ye, 2020. "Relaxed constant positive linear dependence constraint qualification and its application to bilevel programs," Journal of Global Optimization, Springer, vol. 78(1), pages 181-205, September.
    9. Alberto Ramos, 2019. "Two New Weak Constraint Qualifications for Mathematical Programs with Equilibrium Constraints and Applications," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 566-591, November.
    10. Christoph Buchheim & Renke Kuhlmann & Christian Meyer, 2018. "Combinatorial optimal control of semilinear elliptic PDEs," Computational Optimization and Applications, Springer, vol. 70(3), pages 641-675, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:190:y:2021:i:1:d:10.1007_s10957-021-01879-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.